{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:OOZBVCEIY7TVSF6CQFT3JYMLQF","short_pith_number":"pith:OOZBVCEI","schema_version":"1.0","canonical_sha256":"73b21a8888c7e75917c28167b4e18b814818126ce009272f3e972467e2557b43","source":{"kind":"arxiv","id":"2302.14491","version":1},"attestation_state":"computed","paper":{"title":"Formalization of $p$-adic $L$-functions in Lean 3","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.NT","authors_text":"Ashvni Narayanan","submitted_at":"2023-02-28T11:19:22Z","abstract_excerpt":"The Euler--Riemann zeta function is a largely studied numbertheoretic object, and the birthplace of several conjectures, such as the Riemann Hypothesis. Different approaches are used to study it, including $p$-adic analysis : deriving information from $p$-adic zeta functions. A generalized version of $p$-adic zeta functions (Riemann zeta function) are $p$-adic $L$-functions (resp. Dirichlet $L$-functions). This paper describes formalization of $p$-adic $L$-functions in an interactive theorem prover Lean 3. Kubota--Leopoldt $p$-adic $L$-functions are meromorphic functions emerging from the spec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2302.14491","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NT","submitted_at":"2023-02-28T11:19:22Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"dfb1111c82e3acf5c778a474bbef595f621eb5f347dde40257e4f550365f7267","abstract_canon_sha256":"3aa9aed0676807acd286bb4220b32e0d29a375fb94cded7f6a6650c6a6cacd13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:46:45.906191Z","signature_b64":"tfMWwo/Ia1rrppCIm6PXQsaZ5ZpnBbMijZkeSulghSQDCNibfQiC5swS7jICblntCsiRJ/EpNBg/5mX6Stb7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73b21a8888c7e75917c28167b4e18b814818126ce009272f3e972467e2557b43","last_reissued_at":"2026-07-05T05:46:45.905845Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:46:45.905845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formalization of $p$-adic $L$-functions in Lean 3","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.NT","authors_text":"Ashvni Narayanan","submitted_at":"2023-02-28T11:19:22Z","abstract_excerpt":"The Euler--Riemann zeta function is a largely studied numbertheoretic object, and the birthplace of several conjectures, such as the Riemann Hypothesis. Different approaches are used to study it, including $p$-adic analysis : deriving information from $p$-adic zeta functions. A generalized version of $p$-adic zeta functions (Riemann zeta function) are $p$-adic $L$-functions (resp. Dirichlet $L$-functions). This paper describes formalization of $p$-adic $L$-functions in an interactive theorem prover Lean 3. Kubota--Leopoldt $p$-adic $L$-functions are meromorphic functions emerging from the spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.14491","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.14491/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2302.14491","created_at":"2026-07-05T05:46:45.905903+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.14491v1","created_at":"2026-07-05T05:46:45.905903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.14491","created_at":"2026-07-05T05:46:45.905903+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOZBVCEIY7TV","created_at":"2026-07-05T05:46:45.905903+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOZBVCEIY7TVSF6C","created_at":"2026-07-05T05:46:45.905903+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOZBVCEI","created_at":"2026-07-05T05:46:45.905903+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF","json":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF.json","graph_json":"https://pith.science/api/pith-number/OOZBVCEIY7TVSF6CQFT3JYMLQF/graph.json","events_json":"https://pith.science/api/pith-number/OOZBVCEIY7TVSF6CQFT3JYMLQF/events.json","paper":"https://pith.science/paper/OOZBVCEI"},"agent_actions":{"view_html":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF","download_json":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF.json","view_paper":"https://pith.science/paper/OOZBVCEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.14491&json=true","fetch_graph":"https://pith.science/api/pith-number/OOZBVCEIY7TVSF6CQFT3JYMLQF/graph.json","fetch_events":"https://pith.science/api/pith-number/OOZBVCEIY7TVSF6CQFT3JYMLQF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF/action/storage_attestation","attest_author":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF/action/author_attestation","sign_citation":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF/action/citation_signature","submit_replication":"https://pith.science/pith/OOZBVCEIY7TVSF6CQFT3JYMLQF/action/replication_record"}},"created_at":"2026-07-05T05:46:45.905903+00:00","updated_at":"2026-07-05T05:46:45.905903+00:00"}